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SUMMARY:Profinite Rigidity\, Noetherian Domains\, and Solvable Groups - Ju
 lian Wykowski (University of Cambridge)
DTSTART:20250729T104500Z
DTEND:20250729T114500Z
UID:TALK234271@talks.cam.ac.uk
DESCRIPTION:The profinite rigidity of a discrete group &Gamma\; is intimat
 ely related to the profinite rigidity of &Gamma\;-module representations. 
 The quest for understanding the profinite rigidity of groups thus calls fo
 r a systematic theory of profinite rigidity in algebraic categories.\nIn t
 his talk\, I will present a framework for the study of profinite rigidity 
 in the category of modules over a Noetherian domain &Lambda\;. I will expl
 ore profinite invariants for &Lambda\;-modules over any Noetherian domain 
 &Lambda\;\, as well as absolute profinite rigidity results in the presence
  of certain homological assumptions on &Lambda\;. I will then go on to dis
 cuss applications to the profinite rigidity of solvable groups. In particu
 lar\, I will sketch a proof that solvable Baumslag&ndash\;Solitar groups a
 nd free metabelian groups are profinitely rigid in the absolute sense. The
 se are the first known examples of absolute profinite rigidity among non-a
 belian one-relator groups and among non-LERF groups.
LOCATION:Seminar Room 1\, Newton Institute
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